Define the sequence of primes 2,
3, 5, 7, 11, 13, 17, 19, ... as generation 1. Starting from
this generation 1 add the previous and next term
of
each number thus creating generation
2. Apply the same procedure over and over
again to make the next generations
N. The following table summarizes everything
for the first nine generations:

PRIMES
Gen1

Gen2

Gen3

Gen4

Gen5

Gen6

Gen7

Gen8

Gen9

PLOT
Nrs

2

3

7

13

30

56

127

237

530

prime cells

3

7

13

30

56

127

237

530

994

Odd composite

5

10

23

43

97

181

403

757

1662

7

16

30

67

125

276

520

1132

2156

11

20

44

82

179

339

729

1399

2970

13

28

52

112

214

453

879

1838

3598

17

32

68

132

274

540

1109

2199

4491

19

40

80

162

326

656

1320

2653

5335

23

48

94

194

382

780

1544

3136

6231

29

54

114

220

454

888

1816

3578

7278

31

66

126

260

506

1036

2034

4142

8178

37

72

146

286

582

1146

2326

4600

9308

41

80

160

322

640

1290

2566

5166

10290

43

88

176

354

708

1420

2840

5690

11382

2

3

3

3

4

6

5

3

Odd's

With each generation the 'last odd term' moves
down one place (see darkgreen background cells)!
They form a very beautiful new sequence starting with
primes but soon these become very rare: